Many aspects of the later stages of neural development are guided by neuronal activity. Guidance is given both by intrinsic patterns of activity, before and after birth, and by activity resulting from experience after birth. Theoretical studies will address the role of activity-dependent mechanisms in the development of the mammalian cerebral cortex. Such cortical mechanisms appear to play an important role in many aspects of human health, for example in visual disorders such as strabismus and amblyopia, and in recovery and reorganization of somatosensory or motor function after injury or amputation. The theoretical studies will address four specific questions in the development of the primary visual cortex: (l) The relationships that may develop between ocular dominance, preferred orientation, disparity tuning, preferred spatial frequency, and other cortical receptive field properties when inputs of four types (ON-center and OFF-center from the left and right eyes) compete to innervate a two-dimensional cortical layer; (2) The additional effects that are introduced into cortical organization by consideration of the fact that the cortical tissue in which competition occurs is three dimensional, and contains separate inhibitory and excitatory neuronal populations; (3) The effects of interocular correlations on ocular dominance column development, in particular the conditions under which such correlations alter the column width; (4) The changes that are introduced into developmental models when nonlinear cortical activation patterns are introduced, as in the abstract models of cortical development introduced by Kohonen. In all four studies, the goal will be to characterize the different possible developmental outcomes that may result under activity-dependent mechanisms, and the experimentally measurable and manipulable factors that will determine the actual outcome if such mechanisms underlie development. This will provide a basis for experimental tests of the hypothesis that such mechanisms underlie the studied phenomena. An additional long-term goal is to determine the functions of such mechanisms in designing cortical computations. The fourth project, by providing a connection to a set of abstract models whose computational function can be partially characterized, may provide clues to such a functional interpretation of activity-dependent mechanisms in cortical development.